Unit 1 Engineering Physics

4 CHAPTER 1. PROPERTIES OF MATTER

should be at least four times this diameter; 60 mm is common. Gauge length

is used in ductility computations, as discussed in Section 6.6; the standard value is

50 mm (2.0 in.). The specimen is mounted by its ends into the holding grips of the

testing apparatus (Figure 6.3). The tensile testing machine is designed to elongate

the specimen at a constant rate and to continuously and simultaneously measure the

instantaneous applied load (with a load cell) and the resulting elongations (using an

extensometer). A stress–strain test typically takes several minutes to perform and is

destructive; that is, the test specimen is permanently deformed and usually fractured.

[The (a) chapter-opening photograph for this chapter is of a modern tensile-testing

apparatus.]

The output of such a tensile test is recorded (usually on a computer) as load

or force versus elongation. These load–deformation characteristics are dependent

on the specimen size. For example, it will require twice the load to produce the same

elongation if the cross-sectional area of the specimen is doubled. To minimize these

1214 in. 2

6.2 Concepts of Stress and Strain • 153

T

T

F

F

F

F

F

F

F

A 0

A 0

A 0

(a) (b)

(c) (d)

!

"

l l 0 l 0 l

Figure 6.

A standard tensile

specimen with

circular cross

section.

Figure 6.

(a) Schematic

illustration of how a

tensile load produces

an elongation and

positive linear strain.

Dashed lines

represent the shape

before deformation;

solid lines, after

deformation.

(b) Schematic

illustration of how a

compressive load

produces contraction

and a negative linear

strain. (c) Schematic

representation of

shear strain , where

!tan.

(d) Schematic

representation of

torsional

deformation (i.e.,

angle of twist )

produced by an

applied torque T.

f

ug

g

2"

Gauge length

Reduced section

2 "

"Diameter

"

1

4

3

4

(^38) Radius
0.505" Diameter
JWCL187_ch06_150-196.qxd 11/5/09 9:36 AM Page 153
Figure 1.2:Dierent types of load - Dashed lines represent the shape before deformation;
solid lines, after deformation.F= applied external force,A 0 = Area (before deformation)
on which the force is applied.l 0 = length before deformation andl= length after deforma-
tion. (a): Tensile load produces an elongation and positive linear strain, (b): Compressive
load produces contraction and a negative linear strain, (c): Schematic representation of
shear strain“=tan◊, (d): Torsional deformation (i.e., angle of twist„) produced by
an applied torqueT.(Picture courtesy :[ 1 ])

1.2.1 Tensile Test

Tension test can be used to ascertain several mechanical properties of materials that are

important in design. A specimen is deformed up to fracture, with a gradually increasing

tensile load that is applied uniaxially along the long axis of a specimen. A ‘dogbone’

shaped specimen configuration (Figure1.3) was chosen so that, during testing, deforma-

tion is confined to the narrow centre region (which has a uniform cross section along its

length). This choice also to reduces the likelihood of fracture at the ends of the specimen.

The specimen is mounted by its ends into the holding grips of the testing apparatus (Fig-

4